## Degree 4 Ikeda Lifts

We (David Yuen and Cris Poor) have computed many coefficients of Siegel modular cusp forms in degree 4 from weights 8 to 16 that are Ikeda lifts. The Fp polynomials were computed using Katsurada's recursion formula. We thank Oliver King for the use of his Lisp program that implemented this recursion. We used Gordon Nipp's table of quaternary forms that provided genus symbols. The rest of the computations were done with Mathematica.
Please note that the basis of Ikeda lifts given in weights 14 and 16 (where there is more one Ikeda lift) is NOT a basis consisting of Hecke eigenforms. The bases were chosen in these cases to make the coefficients integral. The above only shows the Ikeda lifts. In weights 8 and 10, they span the whole space. (See papers by P-Y.) The dimensions of spaces in weights 12,14,16 are bigger. Namely, dim S_4^12 = 2 (see paper by P-Y.) dim S_4^14 = 3 and dim S_4^16 = 7. (These results will be published in an upcoming paper.)

The following links are versions where the modular forms have been "normalized" so that the coefficients have content 1. And in the case where there is more than one lift, a basis is chosen to make the D4 and A4 coefficients as small as possible while retaining the integrality of the coefficients. The following versions have the coefficients listed in order of determinant.